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A More Efficient 1–Checkable Secure Outsourcing Algorithm for Bilinear Maps

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Information Security Theory and Practice (WISTP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10741))

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Abstract

With the rapid advancements in innovative technologies like cloud computing, internet of things, and mobile computing, the paradigm to delegate the heavy computational tasks from trusted and resource-constrained devices to potentially untrusted and more powerful services has gained a lot of attention. Ensuring the verifiability of the outsourced computation along with the security and privacy requirements is an active research area. Several cryptographic protocols have been proposed by using pairing-based cryptographic techniques based on bilinear maps of suitable elliptic curves. However, the computational overhead of bilinear maps forms the most expensive part of those protocols. In this paper, we propose a new 1–checkable algorithm under the one-malicious version of a two-untrusted-program model. Our solution is approximately twice as efficient as the single comparably efficient 1–checkable solution in the literature, and requires only 4 elliptic curve point additions in the preimage and 6 field multiplications in the image of the bilinear map.

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References

  1. Arabacı, O., Kiraz, M.S., Sertkaya, I., Uzunkol, O.: More efficient secure outsourcing methods for bilinear maps. Cryptology ePrint Archive, Report 2015/960 (2015). http://eprint.iacr.org/2015/960

  2. Barbulescu, R., Duquesne, S.: Updating key size estimations for pairings. Cryptology ePrint Archive, Report 2017/334 (2017). http://eprint.iacr.org/2017/334

  3. Barreto, P., Galbraith, S., Higeartaigh, C., Scott, M.: Efficient pairing computation on supersingular abelian varieties. Des. Codes Cryptogr. 42(3), 239–271 (2007). https://doi.org/10.1007/s10623-006-9033-6

    Article  MathSciNet  MATH  Google Scholar 

  4. Beuchat, J.-L., González-Díaz, J.E., Mitsunari, S., Okamoto, E., Rodríguez-Henríquez, F., Teruya, T.: High-speed software implementation of the optimal ate pairing over Barreto–Naehrig curves. In: Joye, M., Miyaji, A., Otsuka, A. (eds.) Pairing 2010. LNCS, vol. 6487, pp. 21–39. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17455-1_2

    Chapter  MATH  Google Scholar 

  5. Blake, I., Seroussi, G., Smart, N.: Advances in Elliptic Curve Cryptography. London Mathematical Society Lecture Note Series. Cambridge University Press, New York (2005)

    Book  Google Scholar 

  6. Boneh, D., Franklin, M.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_13

    Chapter  Google Scholar 

  7. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the weil pairing. J. Cryptol. 17(4), 297–319 (2004). https://doi.org/10.1007/s00145-004-0314-9

    Article  MathSciNet  MATH  Google Scholar 

  8. Canard, S., Devigne, J., Sanders, O.: Delegating a pairing can be both secure and efficient. In: Boureanu, I., Owesarski, P., Vaudenay, S. (eds.) ACNS 2014. LNCS, vol. 8479, pp. 549–565. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07536-5_32

    Chapter  MATH  Google Scholar 

  9. Chen, X.: Introduction to secure outsourcing computation. Synth. Lect. Inf. Secur. Priv. Trust 8(2), 1–93 (2016)

    Google Scholar 

  10. Chen, X., Susilo, W., Li, J., Wong, D., Ma, J., Tang, S., Tang, Q.: Efficient algorithms for secure outsourcing of bilinear pairings. Theor. Comput. Sci. 562, 112–121 (2015). http://dblp.uni-trier.de/db/journals/tcs/tcs562.html#ChenSLWMTT15

    Article  MathSciNet  Google Scholar 

  11. Chevallier-Mames, B., Coron, J.S., McCullagh, N., Naccache, D., Scott, M.: Secure delegation of elliptic-curve pairing. Cryptology ePrint Archive, Report 2005/150 (2005)

    Google Scholar 

  12. Galbraith, S.D., Paterson, K.G., Smart, N.P.: Pairings for cryptographers. Discrete Appl. Math. 156(16), 3113–3121 (2008)

    Article  MathSciNet  Google Scholar 

  13. Hess, F., Smart, N., Vercauteren, F.: The eta pairing revisited. IEEE Trans. Inf. Theory 52(10), 4595–4602 (2006)

    Article  MathSciNet  Google Scholar 

  14. Hohenberger, S., Lysyanskaya, A.: How to securely outsource cryptographic computations. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 264–282. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30576-7_15

    Chapter  Google Scholar 

  15. Joux, A.: A one round protocol for tripartite Diffie-Hellman. J. Cryptol. 17(4), 263–276 (2004). https://doi.org/10.1007/s00145-004-0312-y

    Article  MathSciNet  MATH  Google Scholar 

  16. Kang, B.G., Lee, M.S., Park, J.H.: Efficient delegation of pairing computation (2005)

    Google Scholar 

  17. Koblitz, N., Menezes, A.: Pairing-based cryptography at high security levels. In: Smart, N.P. (ed.) Cryptography and Coding 2005. LNCS, vol. 3796, pp. 13–36. Springer, Heidelberg (2005). https://doi.org/10.1007/11586821_2

    Chapter  MATH  Google Scholar 

  18. Kumar, K., Liu, J., Lu, Y.H., Bhargava, B.: A survey of computation offloading for mobile systems. Mob. Netw. Appl. 18(1), 129–140 (2013). https://doi.org/10.1007/s11036-012-0368-0

    Article  Google Scholar 

  19. Lin, X.J., Qu, H., Zhang, X.: New efficient and flexible algorithms for secure outsourcing of bilinear pairings. Cryptology ePrint Archive, Report 2016/076 (2016). http://eprint.iacr.org/2016/076

  20. Luo, Y., Fu, S., Huang, K., Wang, D., Xu, M.: Securely outsourcing of bilinear pairings with untrusted servers for cloud storage. In: Trustcom/BigDataSE/ISPA (2016)

    Google Scholar 

  21. Mell, P., Grance, T.: The NIST definition of cloud computing. NIST Special Publication, pp. 800–145 (2011)

    Google Scholar 

  22. Nguyen, P.Q., Shparlinski, I.E., Stern, J.: Distribution of modular sums and the security of the server aided exponentiation (2000)

    Google Scholar 

  23. Ren, Y., Ding, N., Wang, T., Lu, H., Gu, D.: New algorithms for verifiable outsourcing of bilinear pairings. Sci. China Inf. Sci. 59(9), 99103 (2016)

    Article  Google Scholar 

  24. Shacham, H.: New paradigms in signature schemes. Ph.D. thesis, Stanford, CA, USA (2006)

    Google Scholar 

  25. Tian, H., Zhang, F., Ren, K.: Secure bilinear pairing outsourcing made more efficient and flexible. In: Proceedings of the 10th ACM Symposium on Information, Computer and Communications Security, ASIA CCS 2015, pp. 417–426. ACM, New York (2015). https://doi.org/10.1145/2714576.2714615

  26. Wang, Y., Wu, Q., Wong, D.S., Qin, B., Chow, S.S.M., Liu, Z., Tan, X.: Securely outsourcing exponentiations with single untrusted program for cloud storage. In: Kutyłowski, M., Vaidya, J. (eds.) ESORICS 2014. LNCS, vol. 8712, pp. 326–343. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11203-9_19

    Chapter  Google Scholar 

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Correspondence to Öznur Kalkar .

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Kalkar, Ö., Kiraz, M.S., Sertkaya, İ., Uzunkol, O. (2018). A More Efficient 1–Checkable Secure Outsourcing Algorithm for Bilinear Maps. In: Hancke, G., Damiani, E. (eds) Information Security Theory and Practice. WISTP 2017. Lecture Notes in Computer Science(), vol 10741. Springer, Cham. https://doi.org/10.1007/978-3-319-93524-9_10

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  • DOI: https://doi.org/10.1007/978-3-319-93524-9_10

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